The Physical Theory of Hyperfocal Distance and its Application to Photography (cont.)
May, 2010
Ringo Cheung
May, 2010
Ringo Cheung
Abstract
Last time the hyperfocal distance equation in terms of f, N and c was derived from the thin lens formulas. In this article, the relationship between H with f, N and c will be analyzed and some physical inference will be discussed.
Relationship of H with f
Recall that the equation for hyperfocal distance H is given by :
Last time the hyperfocal distance equation in terms of f, N and c was derived from the thin lens formulas. In this article, the relationship between H with f, N and c will be analyzed and some physical inference will be discussed.
Relationship of H with f
Recall that the equation for hyperfocal distance H is given by :
Since H varies with the square of f rather than linearly, a small increase in f will result in a large increase in H. For example, for a 25mm lens of 135 format, H = 2.72m at an aperture of F8; while that for a 50mm lens, H = 10.83m at the same F-stop.
Graph of H vs. f
The 2nd time derivative of H w.r.t. f is :
and the minimum of H exists at f = -Nc/2, the graph concaves upwards. By considering only positive values of f for practical purposes, the graph of H vs. f for 135mm format camera (coc = 0.029) and an F-stop of N = 8 is :
For focal length of 35mm and longer, H is over 5.32m. While this is useful for scene photography, it is not very convenient for street photography and snapshot.
Graph of H vs. N
For a lens of fixed f and c, H is strictly decreasing with N since
as c > 0. On the other hand, a larger f-number means a smaller aperture. Therefore a larger f-number like f8 or f11 will result in a smaller H than with f4. The graph of a 25mm lens (135 format, i.e. coc = 0.029) with f-number from 1 to 16 is depicted below :
which is a hyperbola.
Relationship of H vs. c
Roughly speaking, H is strictly decreasing with c from the hyperfocal distance equation. However, since cameras of different formats have their own definition of wide angle, standard and telephoto lenses, (e.g. a standard 50mm lens in 135 format is considered a wide angle lens in 6x6, 120 format, with c = 0.053) a direct comparison of H vs. c (i.e. different camera formats / film sizes) is not of much practical usefulness.
Conclusion
From the above discussion, a wide angle lens set at small aperture (i.e. a large f-number) is a good candidate for short hyperfocal distance (H) and is more convenient for street and snapshot photos.
